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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2021.tde-30032022-114757
Document
Author
Full name
Nelson Orsalino Neto Schuback
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2021
Supervisor
Committee
Zanata, Salvador Addas (President)
Garcia, Bráulio Augusto
Liu, Xiaochuan
Title in English
A synthesis on classical Brouwer theory
Keywords in English
Brick decompositions
Brouwer lines
Homeomorphisms without fixed points
Maximal decompositions
Abstract in English
In this work we present the fundamentals of Classical Brouwer Theory. We start with the works of L. E. J. Brouwer on translation arcs and the Brouwer translation theo- rem. Next, we explore the notion of maximal free brick decompositions developed by A. Sauzet. Finally, we conclude by presenting a proof of the foliated version of the Brouwer translation theorem, due to P. Le Calvez.
Title in Portuguese
Uma síntese da teoria de Brouwer clássica
Keywords in Portuguese
Decomposições maximais
Decomposições por tijolos
Homeomorfismos sem pontos fixos
Linhas de Brouwer
Abstract in Portuguese
Neste trabalho, nós apresentamos os fundamentos da Teoria de Brouwer Clássica. Nós iniciamos com os trabalhos de L. E. J. Brouwer em arcos de translação e no teorema de translação de Brouwer. Em seguida, nós exploramos o conceito de decomposição em tijolos livre e maximal, desenvolvida por A. Sauzet. Por fim, nós apresentamos a prova de P. Le Calvez da versão folheada do teorema de translação de Brouwer.
 
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disser.pdf (16.63 Mbytes)
Publishing Date
2022-04-01
 
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